Field of the Invention
The present invention relates to a stress analysis apparatus that calculates a residual stress of a sample by using X-ray diffraction measurement results, a method, and a program.
Description of the Related Art
A cos α method, as a stress analysis method by single incidence of X-rays, is known. The cos α method is used in the case where a biaxial stress is analyzed from a single X-ray diffraction image obtained by a two-dimensional detector using the principle to be explained below.
If each symbol is defined as follows, a vertical strain ε(α) of a sample, which is observed at a position of α of a Debye-Scherrer ring, is expressed as expression (1) using vertical strains ε11 and ε22 and a shearing strain ε12 on the device coordinate axes. That is, when a stress field is biaxial, the relationship of expression (1) holds for parameters on the two-dimensional detector.                ψ0: an angle formed by the normal of the sample surface and the incident X-ray        α: a circular angle of the Debye-Scherrer ring on the two-dimensional detector arranged vertical to the incident X-ray        2ηα: an angle formed by the incident X-ray and the diffracted X-ray, there is a relationship of 2ηα=n−2θα with respect to a diffraction angle 2θα,        2θα: a diffraction angle at the position α of the Debye-Scherrer ringε(α)=(sin ψ0 sin θα−cos ψ0 cos α cos θα)2ε11+sin2α cos2θαε22+sin α cos θα(sin ψ0 sin θα−cos ψ0 cos α cos θα)ε12  (1)        
Here, two values εα1 and εα2 are defined as follows.
                              ɛ                      α            ⁢                                                  ⁢            1                          =                                            {                                                ɛ                  ⁡                                      (                    α                    )                                                  -                                  ɛ                  ⁡                                      (                                          π                      +                      α                                        )                                                              }                        +                          {                                                ɛ                  ⁡                                      (                                          -                      α                                        )                                                  -                                  ɛ                  ⁡                                      (                                          π                      -                      α                                        )                                                              }                                2                                    (        2        )                                          ɛ                      α            ⁢                                                  ⁢            2                          =                                            {                                                ɛ                  ⁡                                      (                    α                    )                                                  -                                  ɛ                  ⁡                                      (                                          π                      +                      α                                        )                                                              }                        -                          {                                                ɛ                  ⁡                                      (                                          -                      α                                        )                                                  -                                  ɛ                  ⁡                                      (                                          π                      -                      α                                        )                                                              }                                2                                    (        3        )            
If it is assumed that 2θα or ηα is constant with respect to α, the next relationship is obtained.εα1=S2 sin ψ0 cos ψ0 cos α sin 2ησ11 εα2=S2 sin ψ0 sin α sin 2ησ12  (4)
If the plots of εα1 and εα2 to cos α and sin α are approximated by a straight line based on expression (4), σ11 and σ12 are obtained respectively from the slope. This method is the cos α method.
The cos α method is disclosed in, for example, Non-Patent Literature 1, as a method of finding a local stress from the measurement results by synchrotron X-rays of fiber-reinforced Ti alloy. According to Non-Patent Literature 1, it has been confirmed that the stress at the crack opening, which is obtained from the compression stress distribution calculated by the cos α method, agrees with the measured opening stress.
Further, In Non-Patent Literature 2, the application of the idea of a dilatation term to the expression of stress and strain is also described. In Non-Patent Literature 2, addition of εph of a pseudo hydrostatic strain component to the expression as a dilatation term is described. Then, Non-Patent Literature 2 claims that a stress value may be calculated due to this dilatation term even if the exact lattice constant when stress is zero is not known.
Non-Patent Literature
Non-Patent Literature 1: K. TANAKA, Y. AKINIWA, “Diffraction Measurements of Residual Macrostress and Microstress Using X-Rays, Synchrotron and Neutrons”, JSME International Journal. Series A, v. 47, n. 3, July, 2004, p. 252-263
Non-Patent Literature 2: Baoping Bob He, Kingsley L. Smith, Strain and Stress Measurements with a Two-Dimensional Detector, JCPDS-International Centre for Diffraction Data 1999, P505
As described above, in the cos α method, by taking the constant term of the approximate straight line to be an independent variable, a large error resulting from the error of d0 is removed. However, because the analysis is performed on the assumption that 2θα or ηα, which is originally the function of α, is constant with respect to α, the scattering vector strictly in accordance with the Debye-Scherrer ring is not taken into consideration, and therefore, the calculation results include an error resulting from this assumption.
Further, in the case where the crystal particle size of a sample is coarse, it cannot be avoided to use the Debye-Scherrer ring generated with part of the ring missing as an analysis target, and therefore, it is no longer possible to apply the cos α method. On the other hand, an analysis method using a general expression without approximation such as the cos α method, is conceivable, but it is not possible to solve the expression unless some measures are taken, and if the value of the spacing of crystal lattice planes including an error is used, an error is also included in the calculation results.